Any non default settings you're using?
You didn't really posted much info, guessing I would say you're probably using some pnach file or other memory/disc mod which messes up graphics(like widescreen patches which lately bring all kinds of new troubles as people don't read comments, just download unfinished stuff without thinking;p). It could also be caused by any pcsx2/gsdx mod, if you downloaded pcsx2 from any place different than pcsx2 site or orphis buildbot, it could be modded with some game breaking hacks.

I can only confirm that Persona 4 works just fine on current official builds and doesn't need any special settings to run, hell I even tried to reproduce your bug using harmfull options normal users shouldn't touch(yet often doing it;p) and couldn't cause any glitch like yours.